1. Field of the Invention
The present invention relates to a control unit for controlling an output torque of an induction motor which is used for driving a spindle of a machine tool.
2. Description of the Prior Art
DC motors have been popular up to now because it is easy to control their speeds and torque. However, such DC motors are disadvantageous since they have a very complicated structure because of windings provided in rotors, are rather expensive, and have to be periodically maintained due to worn brushes. Recently, a vector control system has been proposed to control an induction motor, and is effective in controlling an output vector of the induction motor as desired. This control system has enabled induction motors to be frequently adopted to operate a spindle of a machine tool in place of the DC motor. Since they have a simple and durable structure and do not require replacement of brushes, induction motors have come into wide use.
FIG. 1 of the accompanying drawings shows the configuration of one example of a control system for the vector control of a conventional induction motor. This control system receives a torque command T* and a magnetic induction command .phi.* as input commands from an outside source. The magnetic induction command .phi.* is usually a predetermined constant value. However, when it is necessary to suppress a terminal voltage of the motor below a certain level in order to rotate the motor at a high speed, or when the motor should be operated with a reduced magnetic induction, the magnetic induction command .phi.* is varied accordingly. Referring to FIG. 1, a converter 1 generates an excitation current command i1d* in response to the magnetic induction command .phi.*. As will be described later, the excitation current is proportional to the magnetic induction, and has a proportional coefficient which is an inverse of an excitation inductance M. Specifically, the converter 1 multiplies the inverse of the excitation inductance M with the magnetic induction command .phi.*, thereby deriving the excitation current command value i1d*. A divider 2 divides the torque command T* by the magnetic induction command .phi.*. An output torque of the induction motor is proportional to a product of the magnetic induction and the torque current. Thus, an output of the divider 2 is provided as a torque current command value i1q*.
This control unit operates as described hereinafter. Primary current command values iu*, iv* and iw* are expressed as follows using an angular frequency .omega. of a motor current, on the basis of the excitation current command value i1d* and the torque current command value i1q*. This operation is performed by a two-phase-to-3-phase converter 3 shown in FIG. 1. ##EQU1##
The motor current is feedback-controlled by current error amplifiers 4a, 4b and 4c, subtractors 5a, 5b and 5c, and current sensors 6a, 6b and 6c. In other words, primary currents equivalent to the primary current command values iu*, iv* and iw* are introduced into the motor. When an actual excitation current i1d and an actual phase of the torque current i1q in the motor are assumed to be equal to the foregoing excitation current command value i1d* and the phase of the torque current command value i1q*, a combined vector I1 of the primary currents is expressed as follows using i1d and i1q. EQU I1=i1d.multidot.sin .omega.t+i1q.multidot.cos .omega.t (4) EQU I1=(i1d.sup.2 +i1q.sup.2).sup.1/2 .multidot.sin (.omega.t+.theta.2)(5) EQU .theta.2=tan.sup.-1 (i1q/i1d) (6)
FIG. 2 shows a general equalizing circuit in the induction motor. When the primary current I1 flows to the motor, a voltage drop occurs at opposite ends of a primary leakage inductance L.sigma. and a primary resistance r1. Thus, a terminal voltage E1 is generated at a motor terminal. The terminal voltage E1 is expressed by formula (7), where "p" denotes a differential operator d/dt. EQU E1=Em+(p.multidot.L.sigma.+r1)I1 (7)
The second term of equation (7) is very small compared with the first term Em, and is negligible here, thereby deriving equation (8). EQU E1=Em (8)
Em generally denotes a motion electromotive voltage, and has the following relationship with the excitation current i1d of the motor. EQU Em=.omega..multidot.M.multidot.i1d.multidot.cos .omega.t (9)
Referring to the equalizing circuit in FIG. 2, the motion electromotive voltage Em and the torque current i1q have the relationship expressed by equation (10). EQU Em=r2.multidot.i1q/s (but s=.omega.s/.omega.) (10)
In equation 10, .omega.s denotes a slip frequency, and is expressed by equation (11), where .omega.m denotes an angular frequency of the motor. EQU .omega.s=.omega.-.omega.m (11)
In order to control the torque current i1q of the motor to a desired value, the slip frequency .omega.s satisfying equations (10) and (11) should be applied to the motor. Referring to FIG. 1, a divider 7 and a converter 8 provide the slip frequency .omega.s in accordance with the torque current command i1q*.
The foregoing can be paraphrased as follows. The primary current of the motor is feedback-controlled in accordance with the equations (1), (2) and (3). Then, the primary current I1 expressed by equation (4) is controlled to the desired value. At the same time, the slip frequency expressed by the equation (10) is applied to the motor, and the actual torque current i1q of the motor is controlled to the desired value, i.e. i1q*. As expressed by equation (4), the excitation current i1d can be controlled to an optional value.
Torque outputted by the motor will be now considered. An output power P of the motor can be derived by subtracting a loss caused in a secondary resistance r2 from the power applied to a secondary circuit of the motor, as can be seen in the equalizing circuit of FIG. 2. Power Pu for a certain phase is expressed by: EQU Pu=Em.multidot.i1q.multidot.cos .omega.t-r2/s.multidot.i1q.sup.2( 12)
When the loss in the secondary resistance r2 is approximately negligible and the equation (9) is substituted into the equation (12), equation (13) can be derived. EQU Pu=.omega..multidot.M.multidot.i1d.multidot.i1q (cos .omega.t).sup.2( 13)
Considering two-phase powers Pv and Pw for a three-phase motor, Pv and Pw will be expressed by equations (14) and (15), respectively. EQU Pv=.omega..multidot.M.multidot.i1d.multidot.i1q {cos (.omega.t-120.degree.)}.sup.2 ( 14) EQU Pw=.omega..multidot.M.multidot.i1d.multidot.i1q {cos (.omega.t-120.degree.)}.sup.2 ( 15)
A final output power P is derived by summing the powers for the three phases. ##EQU2## Equation (16) can be modified to: EQU P=(3/2).multidot..omega..multidot.M.multidot.i1d.multidot.i1q(17)
When .omega. is approximated to be substantially equal to the motor angular frequency .omega.m, the output torque T of the motor is expressed by: EQU T=P/.omega.m=(3/2).multidot.M.multidot.i1d.multidot.i1q (18)
From the foregoing, when the excitation current i1d and the torque current i1q are controllable to the desired values, the torque T of the motor can be controlled optionally.
The foregoing control unit is prone to the following two problems. Fist of all, although the excitation inductance M is considered to have a certain value, respective motors have their own excitation inductance values, and different motion electromotive voltages Em. The excitation inductance M usually fluctuates with such factors as magnetic saturation of an iron core and precision of sizes of the motor during manufacture. In equation (9) for calculating the speed inducing voltage Em, the excitation inductance M is used as a coefficient. Therefore, if an actual value of the excitation inductance M differs from the value used for the calculation, the derived speed inducing inductance Em inevitably contains an error. Further, the output torque will also contain an error, which means that the motor cannot be controlled accurately.
Secondly, the secondary resistance r2 which is treated as a constant varies with temperature, so the calculated slip s is not always an optimum value. When an operating temperature of the motor is near its upper limit, the secondary resistance r2 becomes twice as large as that at a normal temperature. In equation (10), the secondary resistance r2 is treated as a coefficient. When the secondary resistance r2 varies with temperature, the calculated slip s may differ from the slip s to be actually set. Thus, the motor cannot be reliably and accurately controlled.